Education “reformers” have a common playbook. First, assert without evidence that regular public schools are “failing” and that large numbers of regular (unionized) public school teachers are incompetent. Provide no documentation for this claim other than that the test score gap between minority and white children remains large. Then propose so-called reforms to address the unproven problem – charter schools to escape teacher unionization and the mechanistic use of student scores on low-quality and corrupted tests to identify teachers who should be fired.

The mantra has been endlessly repeated by Secretary of Education Arne Duncan, and by “reform” leaders like former Washington and New York schools chancellors Michelle Rhee and Joel Klein. Bill Gates’ foundation gives generous grants to school systems and private education advocates who adopt the analysis. In Chicago, Mayor Rahm Emmanuel makes the argument, and in New York, Mayor Michael Bloomberg has frequently sung the same tune.

And now, New York Gov. Andrew Cuomo has joined in. On Dr. Martin Luther King Jr.’s birthday last week, the governor cast attacks on unionized teachers as a defense of minority students against the adult bureaucracy. “It’s about the children,” Mr. Cuomo said. Because of failing public schools, “the great equalizer that was supposed to be the public education system can now be the great discriminator.”

But this applause line about school failure is an “urban myth.” The governor, mayor and other policymakers have neglected to check facts they assume to be true. As a result, they may be obsessed with the wrong challenges, while exacerbating real, but overlooked problems.

Careful examination discloses that disadvantaged students have made spectacular progress in the last generation, in regular public schools, with ordinary teachers. Not only have regular public schools not been “the great discriminator” – they continue to make remarkable gains for minority children at a time when our increasingly unequal social and economic systems seem determined to abandon them.

We have only one accurate performance measure. The government administers periodic reading and math tests to samples of fourth, eighth and 12th graders. Called the National Assessment of Educational Progress (NAEP, pronounced “nape”), it is less subject to corruption than standardized tests now legally required of all schoolchildren.

NAEP samples are only large enough to produce reliable national and (for fourth and eighth graders) state estimates, but not for classrooms or schools. Thus, principals or teachers suffer no consequences for poor NAEP scores, giving them no incentive to steal time from instruction to drill on NAEP-type questions.

Not every selected student gets identical NAEP questions. Scores aggregate answers from different students’ booklets, covering different topics from the math and reading curriculums. In contrast, state and city standardized tests change little each year; teachers can predict which of many topics will likely appear, and focus instruction on those.

Here’s what NAEP shows: Average black fourth graders’ math performance in regular public schools has improved so much that it now exceeds average white performance as recently as 1992. The improvement has been greatest for the lowest achievers, those in the bottom 10 percent. Eighth graders show similar, though less dramatic trends. The black-white gap has narrowed little because whites have also improved.

These irrefutable facts characterize both the nation as a whole, and New York State specifically. In fact, New York State’s black children made enormous gains in the 1990’s, and much slower gains once the federal No Child Left Behind, and Mayor Bloomberg’s and Chancellor Klein’s test-based reforms kicked in. From 1992 to 2003, for example, black fourth graders’ math performance jumped 22 scale points (about two-thirds of a standard deviation). From 2003 to 2011, the gain was only 5 scale points.